基于物质点方法(material point method,MPM)理论框架,提出了处理饱和多孔介质与固体间动力接触问题的新方法。其中饱和多孔介质的动力学响应通过文献[1]中发展的耦合物质点方法进行分析,单相固体的力学行为由传统单相物质点方法进行预测。通过本文提出的接触算法使二者相结合,在保证饱和多孔介质与固体间不存在相互穿透的前提下,允许饱和多孔介质与固体间的相互滑动,以预测整个接触/碰撞系统的动力学响应。同时进行了数值算例计算,通过算例验证了此方法的正确性,展示了此方法有效性。
An extended multiscale finite element method （EMsFEM） is developed for solving the mechanical problems of heterogeneous materials in elasticity.The underlying idea of the method is to construct numerically the multiscale base functions to capture the small-scale features of the coarse elements in the multiscale finite element analysis.On the basis of our existing work for periodic truss materials, the construction methods of the base functions for continuum heterogeneous materials are systematically introduced. Numerical experiments show that the choice of boundary conditions for the construction of the base functions has a big influence on the accuracy of the multiscale solutions, thus,different kinds of boundary conditions are proposed. The efficiency and accuracy of the developed method are validated and the results with different boundary conditions are verified through extensive numerical examples with both periodic and random heterogeneous micro-structures.Also, a consistency test of the method is performed numerically. The results show that the EMsFEM can effectively obtain the macro response of the heterogeneous structures as well as the response in micro-scale,especially under the periodic boundary conditions.
Hong-Wu Zhang·Jing-Kai Wu·Jun L·Zhen-Dong Fu State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology,Dalian 116024,China
提出用于饱和多孔介质动力学响应分析的耦合物质点方法(Coupling material point method)。采用u–p形式控制方程对饱和多孔介质进行数值模拟,建立了耦合物质点方法的弱形式离散求解方程,阐述了耦合物质点方法压强场边界条件的处理方式,通过引入边界压强层近似描述指定压强边界,并给出了算法的实施过程。通过数值算例,验证了所提出的耦合物质点方法用于饱和介质动力学分析的正确与有效性。
Based on molecular mechanics and the embedded-atom potential, the torsional mechanical behaviors of metallic copper nanosprings are investigated in this paper. The torsion coefficient of the nanospring is obtained by fitting the curve of potential energy versus torsion angle according to a parabolic law. It is found that the geometry of nanospring has a strong influence on the torsion coefficient. With the increase of the wire radius and the helix radius, the torsion coefficient of the nanospring increases. However, it decreases with the increase of the helix pitch and turns. It is also found that the classic spring theory is invalid to torsional nanosprings. The calculated torsion coefficient is higher than the predication from the classic spring theory and is lower than that of the corresponding solid rod. In addition, the continuum mechanics is shown to be inapplicable to describe the torsional behavior of nanosprings. These findings might provide a better understanding of the usability and functionality of nanosprings in nanodevices.
在传统物质点方法的基础上发展了用于饱和多孔介质动力学分析的两相物质点方法(two-phase material point method,tMPM)。由于饱和多孔介质由固体骨架与孔隙流体组成,两相物质点方法通过引入两套物质点,分别表征固体骨架变形与孔隙流体流动。应用饱和多孔介质u-U形式控制方程,推导了两相物质点方法控制方程离散形式,以固相与液相位移作为基本未知量。采用同传统物质点方法相同的时间积分形式,两相物质点方法成功模拟了饱和多孔介质中固体骨架与孔隙流体间的相互作用;并且通过数值算例中两相物质点方法解与有限元参考解的比较验证了两相物质点方法的正确性。
